Wednesday, July 4, 2007
READING TIME
Although Ethan does not read yet, he really loves his books and enjoys identifying objects. Here he is with his Blue's Clues book...
FUN SUGGESTIONS
from homeschoolfreestuff.
Making Games Work For Kids of All Ages
I always had a problem that the games I wanted our family to play together was either to simple for my older kids, or too complex for my younger ones.
So one day I had an idea!
My younger daughter wanted to play "Chutes and Ladders" for our family game. My older boys didn't want anything to do with it. "It's too easy!", they screamed.So I made a suggestion.
After the game, we go out for a snack. The winner gets to choose the place for the snack. But there's a catch!
My daughter rolls once dice to play, but the middle child has to roll 2, and the oldest has to roll 5. And each child has to get an average! So the middle child has to roll his dice, add them together and divide by 2. The oldest has to roll his 5 dice, add them together and then divide by 5. Each child has to do this within 30 seconds. If they blow the deadline, they have to move back one space.
Let me tell you, this was one intense game of "Chutes and Ladders", everyone had a blast, and it was all they could talk about over our snack at the local McDonalds. The winner's choice!
J. Hall
Making Games Work For Kids of All Ages
I always had a problem that the games I wanted our family to play together was either to simple for my older kids, or too complex for my younger ones.
So one day I had an idea!
My younger daughter wanted to play "Chutes and Ladders" for our family game. My older boys didn't want anything to do with it. "It's too easy!", they screamed.So I made a suggestion.
After the game, we go out for a snack. The winner gets to choose the place for the snack. But there's a catch!
My daughter rolls once dice to play, but the middle child has to roll 2, and the oldest has to roll 5. And each child has to get an average! So the middle child has to roll his dice, add them together and divide by 2. The oldest has to roll his 5 dice, add them together and then divide by 5. Each child has to do this within 30 seconds. If they blow the deadline, they have to move back one space.
Let me tell you, this was one intense game of "Chutes and Ladders", everyone had a blast, and it was all they could talk about over our snack at the local McDonalds. The winner's choice!
J. Hall
Tuesday, July 3, 2007
LESSON ON TIME
I got this for Nikki so he could study time.
This one he answered without difficulty.
Nikki had some difficulty finding the first picture but when I told him to look at all the photos first he got it eventually.
This one he answered without difficulty.
Nikki had some difficulty finding the first picture but when I told him to look at all the photos first he got it eventually.
BUILDING SELF-ESTEEM
http://eqi.org/pare.htm#Other-esteem%20vs.%20self-esteem
To Build Self-Esteem and Bonding
Try to help your children feel:
Acknowledged, admired, appreciated, confident, trusted, needed, important, respected, approved of, heard, safe, supported, understood, independent, free, cared about, valued
Express your feelings rather than issuing commands.
Express your fears. Own them by taking responsibility for them.
Say: "I am afraid you will hurt yourself.", rather than "You are going to kill yourself if you keep that up!"
Take care of yourself. Don't try to get your emotional needs met through your children. That is emotional abuse just as having sex with them is sexual abuse.
Seek first to understand, then be understood.
Show understanding, compassion, empathy. Teach it, model it.
Remember that children are emotional sponges. Infants are pre-logical, all emotional. If you feel negative emotions, they will soak them up even if you try to hide them, so you must work on eliminating them. (the negative feelings, not the kids!)
Become aware of your facial expressions and tone of voice. These carry powerful emotional messages.
Express your regret when you feel it or when you make a mistake. Say: I feel bad about... Let them know it is okay to admit mistakes & normal to feel regret.
Ask their forgiveness. Help them learn to forgive themselves, rather than try to "teach them a lesson they will never forget."
To help them feel confident, don't underestimate them. Let them try more things on their own. Stand back and only offer assistance when it is sought. For example, when a toddler is trying to climb over a fence that his big brother just climbed over, don't just lift him up and put him down on the other side, as I saw a nanny do one day. Instead, stand behind him and make sure he doesn't hurt himself. Even let him fall a few more times than you think you "should." This is also how you help a child not feel overprotected, as many children do. I am amazed to see what happens when children are simply left alone to keep trying. They are incredibly persistent and resilient. They keep trying long after most adults would have given up. I suspect that we have actually been trained to give up and to seek assistance or expect someone else is going to come to the rescue.
Also, teach your older children to let the younger ones do things on their own. I once saw a pre-schooler struggling with buckling her shoes. Her older brother started to do it for her and I said, "Bradley, I think Mary will feel good if she can do that by herself." He said "okay" and soon after she succeeded on her own and briefly looked up to me for recognition. I gave her a wink and a smile to reinforce her proud feeling of accomplishment and independence. I find that sometimes parents exaggerate such small accomplishments and say "Spectacular!" I have mixed feelings about this. It might help a child feel more proud, but it also might set the child up to be approval seeking and externally motivated. It might also diminish the value of positive reinforcement over time, so I feel cautious about verbalizing too much approval, excitement etc. I would be especially cautious if it feels forced to you, as this could be subtly felt as insincerity by an intelligent, sensitive child. Psychologist Nathaniel Branden points out that some children, especially those who are already a bit insecure might think, "They must think I am really pathetic if they have to compliment me for that." Because I want to encourage children to be set their own standards, I tend to follow the child's lead. In other words, I wait to see how the child seems to feel about their effort. If they seem to want recognition, or show that they are proud, I will acknowledge them and their pride. But if they are content without my approval or recognition, I might simply smile to myself, knowing they are becoming independent human beings.
To Build Self-Esteem and Bonding
Try to help your children feel:
Acknowledged, admired, appreciated, confident, trusted, needed, important, respected, approved of, heard, safe, supported, understood, independent, free, cared about, valued
Express your feelings rather than issuing commands.
Express your fears. Own them by taking responsibility for them.
Say: "I am afraid you will hurt yourself.", rather than "You are going to kill yourself if you keep that up!"
Take care of yourself. Don't try to get your emotional needs met through your children. That is emotional abuse just as having sex with them is sexual abuse.
Seek first to understand, then be understood.
Show understanding, compassion, empathy. Teach it, model it.
Remember that children are emotional sponges. Infants are pre-logical, all emotional. If you feel negative emotions, they will soak them up even if you try to hide them, so you must work on eliminating them. (the negative feelings, not the kids!)
Become aware of your facial expressions and tone of voice. These carry powerful emotional messages.
Express your regret when you feel it or when you make a mistake. Say: I feel bad about... Let them know it is okay to admit mistakes & normal to feel regret.
Ask their forgiveness. Help them learn to forgive themselves, rather than try to "teach them a lesson they will never forget."
To help them feel confident, don't underestimate them. Let them try more things on their own. Stand back and only offer assistance when it is sought. For example, when a toddler is trying to climb over a fence that his big brother just climbed over, don't just lift him up and put him down on the other side, as I saw a nanny do one day. Instead, stand behind him and make sure he doesn't hurt himself. Even let him fall a few more times than you think you "should." This is also how you help a child not feel overprotected, as many children do. I am amazed to see what happens when children are simply left alone to keep trying. They are incredibly persistent and resilient. They keep trying long after most adults would have given up. I suspect that we have actually been trained to give up and to seek assistance or expect someone else is going to come to the rescue.
Also, teach your older children to let the younger ones do things on their own. I once saw a pre-schooler struggling with buckling her shoes. Her older brother started to do it for her and I said, "Bradley, I think Mary will feel good if she can do that by herself." He said "okay" and soon after she succeeded on her own and briefly looked up to me for recognition. I gave her a wink and a smile to reinforce her proud feeling of accomplishment and independence. I find that sometimes parents exaggerate such small accomplishments and say "Spectacular!" I have mixed feelings about this. It might help a child feel more proud, but it also might set the child up to be approval seeking and externally motivated. It might also diminish the value of positive reinforcement over time, so I feel cautious about verbalizing too much approval, excitement etc. I would be especially cautious if it feels forced to you, as this could be subtly felt as insincerity by an intelligent, sensitive child. Psychologist Nathaniel Branden points out that some children, especially those who are already a bit insecure might think, "They must think I am really pathetic if they have to compliment me for that." Because I want to encourage children to be set their own standards, I tend to follow the child's lead. In other words, I wait to see how the child seems to feel about their effort. If they seem to want recognition, or show that they are proud, I will acknowledge them and their pride. But if they are content without my approval or recognition, I might simply smile to myself, knowing they are becoming independent human beings.
Monday, July 2, 2007
A HEARTWARMING LETTER
http://www.home-school.com/Articles/phs15-joshuaharris.html
Thanks, Mom & Dad
By Joshua HarrisPrinted in PHS #15, 1997.
I can hardly believe it - I'm leaving home. Three months from now I'll be packing up my little Civic Wagon and saying goodbye to my parents and five younger siblings. I don't think the weight of it has really hit me yet. I'm used to going away on short trips. "See you next week!" This is different. I'm going away forever (at least as far into forever as I can see) to start a new life on the other side of the country.
The move is bittersweet. I know it's God's will and my parents fully support it, but it's still hard. I get teary-eyed over funny things - my little brother barging into my room each morning, coming home from work and seeing my mom framed in the window, chatting on the phone with a friend. The scenes seem to play in slow motion, reminding me that I'm leaving them behind.
You've heard the line before: "You never know what you've got till you lose it." I never realized how true this statement is until now. I've taken so many things about my parents for granted. Lately I've been reflecting on some of the things I appreciate most about the way they raised me. There are three things that I've been especially grateful for recently.
They raised me without television.
My parents both grew up in homes where the television was constantly on. It was on during dinner, it was the background noise throughout the day. When my folks got married they decided they would raise their kids in a TV-free home.
This might seem like a funny thing to be thankful for, and there were times in my life when I wasn't appreciative. I used to long for Saturday morning cartoons and feel out of it when I was the only kid at church who didn't know every sitcom theme song by heart. But my gratefulness for this simple decision has grown over the years. As I look back on the countless evenings we spent reading as a family, that flashing box seems a sorry substitute. Ramona Quimby, Ralph Moody, and the children who visited Narnia kept us enthralled instead.
My parents placed a priority on doing things as a family, things that engaged the mind and allowed us to share life. People ask if the reason for not having a TV was the bad programming. Certainly that's part of it, but the primary problem with TV in their opinion, is not the bad things that are watched, it's the good things you're not doing while you watch - the books that go unread and the stories that go untold. I'm thankful my parents chose books and conversations over television.
They taught me to paddle my own boat.
When I was fourteen I wanted to be an actor. Thankfully, this aspiration was short-lived. But I'll never forget the conversation I had with my dad during this time. I was cooking up schemes to one day be a star in Hollywood, when my father sat me down and said, "Son, I never want you to be in a position where you're going around knocking on people's doors asking to be a part of what they're doing. I don't want you to pursue a career where you're waiting for someone else to give you the 'big break.' If you want to start your own Christian acting troupe, go for it, but I don't want you to be the kind of person who sits around waiting for someone else to make things happen for you."
I'm still discovering the value of this attitude. I wasn't always teachable, but my dad's entrepreneurial and adventurous spirit rubbed off on me. Armed with it I've run head-long into the diverse pursuits of everything from a pen-pal company, to videography, to magazine publishing. All these endeavors stemmed from a simple conviction that I didn't have to wait for my ship to come in, I could pick up the oars in my little boat and start paddling. My dad taught me that.
They were willing to let go.
The move I mentioned earlier is to Gaithersburg, Maryland. For the past year God has been leading me in a new direction. He's been drawing my heart to the local church. So I'm laying down my pursuit of magazine publishing to learn how my gifts can be used in the context of a local body of believers. The pastors at Covenant Life Church will be discipling and training me. It's sort of an "apprenticeship" in ministry. The tough part in all this is that Covenant Life is several thousand miles away from my current home in Gresham, Oregon.
I could not have pursued this venture without my parent's willingness to see God's will done. Our family's comfort is not their primary concern. I'm their son, but first I'm God's servant. That example has been an inspiration. The humility my mom and dad have shown in allowing me to pursue this new direction is equally inspiring. I listened while my father told the pastor I'll be serving under that there are some things he can't teach me. "I believe you can instruct Josh in ways he wouldn't get if he stayed here."
Thanks, Mom and Dad, for raising me in the fear and admonition of the Lord; for modeling by example what it means to serve Him. And finally, for being my cheering section as I set out on this adventure of life.
Thanks, Mom & Dad
By Joshua HarrisPrinted in PHS #15, 1997.
I can hardly believe it - I'm leaving home. Three months from now I'll be packing up my little Civic Wagon and saying goodbye to my parents and five younger siblings. I don't think the weight of it has really hit me yet. I'm used to going away on short trips. "See you next week!" This is different. I'm going away forever (at least as far into forever as I can see) to start a new life on the other side of the country.
The move is bittersweet. I know it's God's will and my parents fully support it, but it's still hard. I get teary-eyed over funny things - my little brother barging into my room each morning, coming home from work and seeing my mom framed in the window, chatting on the phone with a friend. The scenes seem to play in slow motion, reminding me that I'm leaving them behind.
You've heard the line before: "You never know what you've got till you lose it." I never realized how true this statement is until now. I've taken so many things about my parents for granted. Lately I've been reflecting on some of the things I appreciate most about the way they raised me. There are three things that I've been especially grateful for recently.
They raised me without television.
My parents both grew up in homes where the television was constantly on. It was on during dinner, it was the background noise throughout the day. When my folks got married they decided they would raise their kids in a TV-free home.
This might seem like a funny thing to be thankful for, and there were times in my life when I wasn't appreciative. I used to long for Saturday morning cartoons and feel out of it when I was the only kid at church who didn't know every sitcom theme song by heart. But my gratefulness for this simple decision has grown over the years. As I look back on the countless evenings we spent reading as a family, that flashing box seems a sorry substitute. Ramona Quimby, Ralph Moody, and the children who visited Narnia kept us enthralled instead.
My parents placed a priority on doing things as a family, things that engaged the mind and allowed us to share life. People ask if the reason for not having a TV was the bad programming. Certainly that's part of it, but the primary problem with TV in their opinion, is not the bad things that are watched, it's the good things you're not doing while you watch - the books that go unread and the stories that go untold. I'm thankful my parents chose books and conversations over television.
They taught me to paddle my own boat.
When I was fourteen I wanted to be an actor. Thankfully, this aspiration was short-lived. But I'll never forget the conversation I had with my dad during this time. I was cooking up schemes to one day be a star in Hollywood, when my father sat me down and said, "Son, I never want you to be in a position where you're going around knocking on people's doors asking to be a part of what they're doing. I don't want you to pursue a career where you're waiting for someone else to give you the 'big break.' If you want to start your own Christian acting troupe, go for it, but I don't want you to be the kind of person who sits around waiting for someone else to make things happen for you."
I'm still discovering the value of this attitude. I wasn't always teachable, but my dad's entrepreneurial and adventurous spirit rubbed off on me. Armed with it I've run head-long into the diverse pursuits of everything from a pen-pal company, to videography, to magazine publishing. All these endeavors stemmed from a simple conviction that I didn't have to wait for my ship to come in, I could pick up the oars in my little boat and start paddling. My dad taught me that.
They were willing to let go.
The move I mentioned earlier is to Gaithersburg, Maryland. For the past year God has been leading me in a new direction. He's been drawing my heart to the local church. So I'm laying down my pursuit of magazine publishing to learn how my gifts can be used in the context of a local body of believers. The pastors at Covenant Life Church will be discipling and training me. It's sort of an "apprenticeship" in ministry. The tough part in all this is that Covenant Life is several thousand miles away from my current home in Gresham, Oregon.
I could not have pursued this venture without my parent's willingness to see God's will done. Our family's comfort is not their primary concern. I'm their son, but first I'm God's servant. That example has been an inspiration. The humility my mom and dad have shown in allowing me to pursue this new direction is equally inspiring. I listened while my father told the pastor I'll be serving under that there are some things he can't teach me. "I believe you can instruct Josh in ways he wouldn't get if he stayed here."
Thanks, Mom and Dad, for raising me in the fear and admonition of the Lord; for modeling by example what it means to serve Him. And finally, for being my cheering section as I set out on this adventure of life.
Sunday, July 1, 2007
SELF-ESTEEM
http://www.cyh.com/HealthTopics/HealthTopicDetails.aspx?p=114&np=141&id=1702
SELF-ESTEEM
Self-esteem is feeling good about yourself, feeling that you are a worthwhile person. While we all have doubts at times, it is important for children to feel OK about themselves most of the time. Self-esteem enables them to try new things without too much fear of failing, to reach out and make friends, and to manage problems they are likely to meet along the way. Good self-esteem builds a solid foundation for life.
What is self-esteem?
Self-esteem is liking yourself. It is not conceit or boastfulness, but believing in yourself and what you do.
Self-esteem is how you feel about yourself as a person and knowing that there are things that you can do well - in other words it is about being and about doing.
Part of self-esteem is feeling that you have a place in the world where you belong - that you are part of a family where you matter. It is knowing about your roots and having confidence in your future. This can be a problem for children who have come from other countries and lost touch with their "roots". It can also be a problem for children who have been part of a family break up if they are split off from part of their family and the history of that part of the family.
Self-esteem is about what matters to you. If you want to be good at sport but everyone tells you that you are good at art, it will not help your self-esteem very much. If you get encouragement and help in something you want to do, and you succeed, your self-esteem will grow.
How self-esteem is developed
Babies
Very young babies don't have a sense of themselves as being separate human beings so they don't really have self esteem as such. They gradually learn that they are loved and lovable because people care for them gently, look after them when they cry and smile at them consistently. When this happens it says to the baby - "you matter in the world".
Toddlers
As infants grow to become toddlers, they still don't have a complete understanding about themselves. For example, if a one year old is standing on the end of a rope that she is trying to pull, she may not move her feet off the rope. This is because she doesn't yet realise that both the feet and the hands belong to her. One year olds still don't understand that all of their body and mind belong to them. Every time they learn a new skill they add to their sense of being able to do things and learning who they are.
When they say "No" they are really saying "I am learning that I am a separate person and this is very exciting and important for me. I can practise this by saying "No" even if I do want the icecream that you are giving me."
Toddlers learn about themselves by learning what they look like, what they can do and where they belong. They find it very difficult to share because they are just learning who they are and what is theirs.
Toddlers see themselves through their parents' eyes. If their parents see them as special and lovable and show them and tell them this often, they will develop self esteem. If they keep getting messages that they are not lovable or a nuisance they will not so easily develop self-esteem.
Pre-schoolers
By three or so children have learned that their bodies and minds are their own. They can manage time away from their parents or main caregivers because they have an inner sense of feeling safe. They still learn their self esteem in fairly physical ways, by comparing themselves with others, eg. who is the tallest, who is the fastest.
Primary school-age children
Many children's self-esteem falls when they start school and have to cope in a strange new situation with lots of other new children and new rules to learn. Self-esteem in the primary school years is about how well children manage the learning tasks of the school, how they do at sport, how they look and how they can make friends with other children. Stresses at home such as parents fighting with each other can affect children's self-esteem. So can problems at school such as having trouble with schoolwork, being bullied or not having friends.
What parents can do
For almost all parents there are times when you worry about your child's self-esteem.
Here are some things you can do to help.
Messages that help destroy children's self-esteem
Resources
Books for Parents
Baron S, Ingham K "21 ways to build your teenagers self esteem.... and enjoy being a parent again" 1995.
References
Gilligan, R. "Adversity, resilience and young people: the protective value of positive school and spare time experiences" in Children & Society, 14 (2000), 37-47.
Davis-Kean, Pamela and Sandler H. "A Meta-analysis of measure of self-esteem for young children: a framework for future measures" in Child Development May/June 2001 72 (3) 887-906.
SELF-ESTEEM
Self-esteem is feeling good about yourself, feeling that you are a worthwhile person. While we all have doubts at times, it is important for children to feel OK about themselves most of the time. Self-esteem enables them to try new things without too much fear of failing, to reach out and make friends, and to manage problems they are likely to meet along the way. Good self-esteem builds a solid foundation for life.
What is self-esteem?
Self-esteem is liking yourself. It is not conceit or boastfulness, but believing in yourself and what you do.
Self-esteem is how you feel about yourself as a person and knowing that there are things that you can do well - in other words it is about being and about doing.
Part of self-esteem is feeling that you have a place in the world where you belong - that you are part of a family where you matter. It is knowing about your roots and having confidence in your future. This can be a problem for children who have come from other countries and lost touch with their "roots". It can also be a problem for children who have been part of a family break up if they are split off from part of their family and the history of that part of the family.
Self-esteem is about what matters to you. If you want to be good at sport but everyone tells you that you are good at art, it will not help your self-esteem very much. If you get encouragement and help in something you want to do, and you succeed, your self-esteem will grow.
How self-esteem is developed
Babies
Very young babies don't have a sense of themselves as being separate human beings so they don't really have self esteem as such. They gradually learn that they are loved and lovable because people care for them gently, look after them when they cry and smile at them consistently. When this happens it says to the baby - "you matter in the world".
Toddlers
As infants grow to become toddlers, they still don't have a complete understanding about themselves. For example, if a one year old is standing on the end of a rope that she is trying to pull, she may not move her feet off the rope. This is because she doesn't yet realise that both the feet and the hands belong to her. One year olds still don't understand that all of their body and mind belong to them. Every time they learn a new skill they add to their sense of being able to do things and learning who they are.
When they say "No" they are really saying "I am learning that I am a separate person and this is very exciting and important for me. I can practise this by saying "No" even if I do want the icecream that you are giving me."
Toddlers learn about themselves by learning what they look like, what they can do and where they belong. They find it very difficult to share because they are just learning who they are and what is theirs.
Toddlers see themselves through their parents' eyes. If their parents see them as special and lovable and show them and tell them this often, they will develop self esteem. If they keep getting messages that they are not lovable or a nuisance they will not so easily develop self-esteem.
Pre-schoolers
By three or so children have learned that their bodies and minds are their own. They can manage time away from their parents or main caregivers because they have an inner sense of feeling safe. They still learn their self esteem in fairly physical ways, by comparing themselves with others, eg. who is the tallest, who is the fastest.
Primary school-age children
Many children's self-esteem falls when they start school and have to cope in a strange new situation with lots of other new children and new rules to learn. Self-esteem in the primary school years is about how well children manage the learning tasks of the school, how they do at sport, how they look and how they can make friends with other children. Stresses at home such as parents fighting with each other can affect children's self-esteem. So can problems at school such as having trouble with schoolwork, being bullied or not having friends.
What parents can do
For almost all parents there are times when you worry about your child's self-esteem.
Here are some things you can do to help.
- Tell your child often that you love her and let her see that you are glad she is who she is.
- Show your child that you love her by spending time with her, listening to her point of view, and being willing to help her achieve her goals, eg. drive her to sport and watch when she plays.
- Support her school work - take an interest without taking over. Support school working bees or tuck shop if you can.
- Encourage friendships and make her friends welcome and get to know them.
- If she needs extra help with school work try to provide this but don't make all her life practise at what she is not good at - children need to practise what they are good at to feel successful.
- Talk with the teacher. A good relationship between school and home is very important.
- Help your child to explore any hobbies that she is interested in.
- Help your child feel that she is needed in your family. Within reason for the child's age, ask and expect some help with the family chores such as feeding pets, setting the table etc (not just clean up her own mess but contribute to the family).
- Let your child assist you with something eg teenagers may be better than you at making the video work.
- When you play games with your primary school age child make sure that she has opportunities to win. If children win sometimes it is easier for them to learn to be good losers.
- Involve them in the wider family; help them to know their relatives and about your family and its history.
- Keep special mementoes of their successes and important milestones.
- Keep little family rituals eg story at bedtime, kiss goodbye and the other ways of doing things that are special to your family.
- Celebrate achievements and successes.
- Don't solve all problems for your child. Help her learn problem solving skills and learn to feel that she can manage many things for herself. Show her that you have faith in her.
Messages that help destroy children's self-esteem
- Ignoring them and not taking an interest in them.
- Messages that say you do not like the child eg "I love you but I don't like you."
- "You are..." messages that say something bad about them as people eg "You are...lazy, untidy, naughty, a nuisance, a bully, shy, a sook....."
- Comparing them with others, especially brothers and sisters.
- Giving messages that life would be better without them eg "If it weren't for the children we could have a good holiday" or "I wish you hadn't been born."
- Threatening to leave them if they do not do as you wish.
- Frowning and/or sighing when they want to talk to you or ask you for something.
Resources
Books for Parents
Baron S, Ingham K "21 ways to build your teenagers self esteem.... and enjoy being a parent again" 1995.
References
Gilligan, R. "Adversity, resilience and young people: the protective value of positive school and spare time experiences" in Children & Society, 14 (2000), 37-47.
Davis-Kean, Pamela and Sandler H. "A Meta-analysis of measure of self-esteem for young children: a framework for future measures" in Child Development May/June 2001 72 (3) 887-906.
MATH
http://www.home-school.com/Articles/phs28-marypride.html
How to Succeed With Math
By Mary PridePrinted in PHS #28, 1999.
When we were kids, growing up in different states, Bill and I both enjoyed solving math puzzles and creating math challenges for ourselves. Yet we saw the kids around us struggling with math, claiming it was too hard and that they hated it.
I didn't believe this. How could anyone hate math? And how could math be "hard" when it was so logical?
Bill went to M.I.T., where he earned a degree in math; I was a math major at Boston College before I transferred to R.P.I. and switched to engineering. We eventually met , got married, and had kids, who we homeschooled. All of our children have gone on to do well in math. Most of them have already won, or placed in the top three, of at least one local and or national math competition.
This sounds like annoying bragging, doesn't it? Bear with me. I'm not saying that our kids are all genetic math geniuses. In fact, if they were in school, at least three would have been diagnosed with ADD, and one with dyslexia. We haven't had a tremendous amount of time to spend drilling them on math, either. Thanks to my duties at PRACTICAL HOMESCHOOLING, I actually have less time to spend on such things than the average homeschool mom.
What I do have is my dad the college professor, who taught me to be analytical about how I learned things from a very early age. I remember how he got me excited about math, what helped me learn the quickest, and what was a massive waste of time. I also had the tremendous experience of him teaching me six grades of math (from grade 2 through grade 7) in the summer after first grade. So even before I began homeschooling, I knew math could be taught much more quickly and effortlessly than almost anyone believes today. For what I am about to share with you, I am indebted to Dr. Stuart Martin of Boston College, my father.
Competition & Rewards
Let's start at the beginning, with motivation. Competition and rewards, as much as some people like to knock them, were a big factor in both Bill and me getting turned on to math. My dad offered me, at the age of five, a penny for every page I completed in a set of math workbooks he bought me. After I had very quickly earned a buck, he declined to issue any further remuneration, but by then I had learned (1) I could do this! and (2) math was fun and profitable!
In Bill's case, his third-grade teacher had her class copy out four pages of math problems each week. Every Wednesday, they would have a timed math bee, filling in the problems. The first person to get them all right was the winner. A clickable ball-point pen (then costing around 5¢) was the prize. Bill only won about once every five weeks, but that was enough to motivate him to start thinking about math as an exciting game.
The idea is to make a child's first math experience a thrill. Some variations: do math problems with M&Ms, and let them eat the answers they get right. Let them do math with pennies, and keep the change if they get the problem right. You won't want to keep doing this for months at a time, as the kids will either get fat or rich, but as my dad found, it isn't necessary to keep up these rewards once the children start enjoying math for its own sake.
The Barnum Software Quarter Mile program brings just this surge of excitement. Not only are kids drilling the math facts, they are competing against their own previous best speeds. This can be taken to a competitive level if you sign up for one of their International Math Tournaments. Our kids all enjoyed competing very much, and it certainly gave them incentive to practice! For a noncomputerized alternative, the Providence Project Calculadder timed math drill sheets also "rev" kids up and give them that sense of progress.
The great beauty of math drill software is that you, the devoted parent, don't have to be there for the child to improve his skills. But if you prefer to use traditional flashcard, here's a tip: let the child hold the cards he gets right, then run through the deck again. Every time he gets a card, the number of facts to drill narrows down to those that need the most work; and for some reason, holding the cards make the child feel like a winner. He will count the cards he has gotten right so far (more math practice!) and calculate how many he has to go (yet more practice!), while feeling he has already succeeded at least in part.
What Counts?
Most of us have 10 fingers and 10 toes to count. But that gets old pretty fast. Try counting backwards, like a rocket lift-off countdown: "10, 9, 8, 7, 6, 5, 4, 3, 2, 1, BLAST OFF!" Little kids love it! Try learning to count in several foreign languages. This is a great way to introduce the concept of other languages, and to help kids keep their ability to make the sounds of languages other than our own. It also teaches them that "2" is "2," no matter what it's called.
I have a dress with 20 buttons. This made it easy to practice counting with teeny-tiny ones on my lap. Try counting flowers on the wallpaper, leaves on a branch, cans on the shelf . . . whatever is right there in front of you. Remember to make a big excited fuss when the little one gets it right!
Math Manipulatives
For the math facts, I still think money makes the best math manipulatives. Coins and bills aren't rods you can lay side by side, or cubes you can snap together. For that very reason, they encourage abstract math thinking skills. A dime doesn't look like it's worth more than a nickel; it just is worth more than a nickel. You have to assign a value of 10 to the dime and 5 to the nickel. This is prealgebra and advanced math at its most basic; assigning values and making calculations based on those values.
A word more about the value of abstract thinking. The National Council of Teachers of Mathematics has been for some time promoting the use of hands-on math manipulatives designed to help children think about math concretely. "This five-rod is as long as five one-rods. I can see with my eyes how many one-rods it takes to make a rod of the same length as one five-rod." This is not the way math manipulatives have worked throughout history. The sheepherder who made a knot in his string for every ten sheep, or the abacus user who moved a bead to the top of his abacus to indicate "five," were using the knot or the bead to indicate abstract value. There is nothing "ten-ish" about a knot, or "five-ish" about a bead, any more than there is anything "ten-ish" about a dime or "five-ish" about a nickel. People had to think abstractly to handle the knots and beads. They couldn't just count up a number of one-rods to get the answer.
A dime does not resemble ten pennies in the least. A ten-rod resembles ten one-rods; maybe not in its color, but in having the exact same overall length and shape. Therefore, I encourage you to use rods, cubes, and even cuter manipulatives such as the Delta Fast Food math items reviewed elsewhere in this issue, to demonstrate math principles, but not to work math problems. Rather, try using coins, with all their different values. Your kids will learn the most essential math skill of all, needed in all math from algebra on up - how to solve problems where you can't simply count your way to the answer. At the moment, it will be a nickel standing for five pennies; later, it will be x standing for a number; still later, it will be x standing for an entire statement including other variables; later yet, it will be f(x) standing for a series, or a number set, or the area under a curve, and so on. All of this is really easy if you understand the concept of abstract value. But I guarantee you that a child who has always been able to stick manipulatives end-to-end or in a square to solve a problem will be totally lost when he runs into negative numbers, irrational numbers, or imaginary numbers. Don't get stuck in the concrete, when you could teach your children abstract math thinking with your pocket change.
One more point about money: even kids who struggle with numbers catch on very quickly when those numbers have two decimal places and dollar signs. I have yet to meet a kid who can't learn to shop!
Girls & Math
Research shows that American girls do noticeably worse than American boys on standardized math tests. But not homeschooled girls! Our own daughter Sarah recently scored a perfect 80 out of 80 on the math portion of the PSAT. (I admit it, that was bragging!)
The better performance of homeschooled girls probably has to do with (1) using math more in their everyday lives and (2) not being surrounded by boys who not-so-subtly prefer cute airheads to smart young misses. As long as the parents expect their daughter to do well in math, there should be nothing in the homeschool environment to hold her back.
One area that most girls do need extra help with, even at home: spatial skills. If I ask you to visualize a shape in your head, then rotate it various ways, most guys can do this with ease, but most gals can't. Two resources I have found that are a great help in improving spatial skills are:
F The Factory (Mac, Win, Apple, and DOS versions available; $89.95) and Factory Deluxe (Mac or Win CD; $89.95) software from Sunburst (1-800-321-7511). Or (for Mac only, $129.95) the Spatial Sense CD-ROM, which includes Factory, Super Factory, and Building Perspective. Check them out on www.sunburst.com.
F The most excellent D.I.M.E. Blocks ($17) and associated 3-D Build-Up books (three available for $7 each) from Timberdoodle (1-360-426-0672). This forms an entire mini-course in spatial skills, as you rotate and fit the odd-shaped blocks together. Oodles of fun, too!
Puzzles & Construction
Puzzles and construction toys are another great way to develop your spatial skills. Bill's mom was, and is, an avid puzzler, who also bought him Tinkertoys and Erector sets. Oddly enough, my parents also gave me tons of puzzles, and the very same building sets Bill grew up with.
Today, "Erector" sets are called "Meccano," and products such as Duplo and Lego bricks are mainstays of many homeschools. While Lego-like products are great for creativity, they only fit together in a few limited ways. For more advanced spatial and engineering skills, an up-to-date construction series such as Fishertechnik (available from Timberdoodle: 1-360-426-0672) or the motorized Robotix kits (available from Home Life: 1-800-346-6322) is what you need.
A Word About Words
One fact of mathematical life that nobody talks about is the nomenclature: the jargon mathematicians use. Getting a grip on the lingo as early as possible is a way for your child to "pre-digest" some of what he'll be encountering in later math courses. We were only kidding about the Baby's First Calculus course in our Homeschool Admirer parody section in this issue, because babies can't learn calculus. However, young kids can learn calculus terminology. So go ahead: "integrate" these math words into your daily life and help your children "function" better as you push them to their "limits"! (Note: the words in quotes are mathematical terms. I don't really think kids should be pushed anywhere unless they're in a baby carriage or wheelchair.)
A great book I just found that can help you with this is G is for Googol, from Tricycle Press pictured on the first page of this article ($15.95, 1-800-841-2665). This "alphabet" book is not for teaching little kiddies to read. Instead, this 57-page, oversized, fully illustrated hardcover is devoted to explaining advanced math to the young. Starting with "A is for abacus," in which we see an abacus, learn its history, and see how it works, each letter stands for one or more important topics beloved of mathematicians. I'm not talking about wimpy stuff like addition or fractions, either. Cast your ovoid oculars on this list:
Abacus, Binary, Cubit, Diamond, Equilateral, Exponent, Fibonacci, Googol, Googolplex, Hundred, "If," Jupiter, K?sberg, Light-year, M?s Strip, Nature, Obtuse, Probability, Quantity and Quality, Rhombicosidodecahedron, Symmetry, Tesselate, Unit, Venn Diagram, "When are we ever going to use this stuff, anyway?," X, Y-axis, Zillion.
Each concept is explained in easy-reading detail, with full-color drawings and diagrams. As a bonus, for each letter you'll also find a list of other math concepts starting with the letter in question. So A is for Abacus (the main entry), and also for acute, algebra, angle, art, architecture, area, asymmetry, average, and axis. No definitions are provided for the bonus list, but any parent with a smidgen of mathematical training can use this list for inspiration for further explanations and explorations.
Three last tips: (1) math puzzle books, available at bookstores and teacher's stores: (2) checkers, and (3) chess. All are great, fun ways to improve math thinking skills. Let's do it!
How to Succeed With Math
By Mary PridePrinted in PHS #28, 1999.
When we were kids, growing up in different states, Bill and I both enjoyed solving math puzzles and creating math challenges for ourselves. Yet we saw the kids around us struggling with math, claiming it was too hard and that they hated it.
I didn't believe this. How could anyone hate math? And how could math be "hard" when it was so logical?
Bill went to M.I.T., where he earned a degree in math; I was a math major at Boston College before I transferred to R.P.I. and switched to engineering. We eventually met , got married, and had kids, who we homeschooled. All of our children have gone on to do well in math. Most of them have already won, or placed in the top three, of at least one local and or national math competition.
This sounds like annoying bragging, doesn't it? Bear with me. I'm not saying that our kids are all genetic math geniuses. In fact, if they were in school, at least three would have been diagnosed with ADD, and one with dyslexia. We haven't had a tremendous amount of time to spend drilling them on math, either. Thanks to my duties at PRACTICAL HOMESCHOOLING, I actually have less time to spend on such things than the average homeschool mom.
What I do have is my dad the college professor, who taught me to be analytical about how I learned things from a very early age. I remember how he got me excited about math, what helped me learn the quickest, and what was a massive waste of time. I also had the tremendous experience of him teaching me six grades of math (from grade 2 through grade 7) in the summer after first grade. So even before I began homeschooling, I knew math could be taught much more quickly and effortlessly than almost anyone believes today. For what I am about to share with you, I am indebted to Dr. Stuart Martin of Boston College, my father.
Competition & Rewards
Let's start at the beginning, with motivation. Competition and rewards, as much as some people like to knock them, were a big factor in both Bill and me getting turned on to math. My dad offered me, at the age of five, a penny for every page I completed in a set of math workbooks he bought me. After I had very quickly earned a buck, he declined to issue any further remuneration, but by then I had learned (1) I could do this! and (2) math was fun and profitable!
In Bill's case, his third-grade teacher had her class copy out four pages of math problems each week. Every Wednesday, they would have a timed math bee, filling in the problems. The first person to get them all right was the winner. A clickable ball-point pen (then costing around 5¢) was the prize. Bill only won about once every five weeks, but that was enough to motivate him to start thinking about math as an exciting game.
The idea is to make a child's first math experience a thrill. Some variations: do math problems with M&Ms, and let them eat the answers they get right. Let them do math with pennies, and keep the change if they get the problem right. You won't want to keep doing this for months at a time, as the kids will either get fat or rich, but as my dad found, it isn't necessary to keep up these rewards once the children start enjoying math for its own sake.
The Barnum Software Quarter Mile program brings just this surge of excitement. Not only are kids drilling the math facts, they are competing against their own previous best speeds. This can be taken to a competitive level if you sign up for one of their International Math Tournaments. Our kids all enjoyed competing very much, and it certainly gave them incentive to practice! For a noncomputerized alternative, the Providence Project Calculadder timed math drill sheets also "rev" kids up and give them that sense of progress.
The great beauty of math drill software is that you, the devoted parent, don't have to be there for the child to improve his skills. But if you prefer to use traditional flashcard, here's a tip: let the child hold the cards he gets right, then run through the deck again. Every time he gets a card, the number of facts to drill narrows down to those that need the most work; and for some reason, holding the cards make the child feel like a winner. He will count the cards he has gotten right so far (more math practice!) and calculate how many he has to go (yet more practice!), while feeling he has already succeeded at least in part.
What Counts?
Most of us have 10 fingers and 10 toes to count. But that gets old pretty fast. Try counting backwards, like a rocket lift-off countdown: "10, 9, 8, 7, 6, 5, 4, 3, 2, 1, BLAST OFF!" Little kids love it! Try learning to count in several foreign languages. This is a great way to introduce the concept of other languages, and to help kids keep their ability to make the sounds of languages other than our own. It also teaches them that "2" is "2," no matter what it's called.
I have a dress with 20 buttons. This made it easy to practice counting with teeny-tiny ones on my lap. Try counting flowers on the wallpaper, leaves on a branch, cans on the shelf . . . whatever is right there in front of you. Remember to make a big excited fuss when the little one gets it right!
Math Manipulatives
For the math facts, I still think money makes the best math manipulatives. Coins and bills aren't rods you can lay side by side, or cubes you can snap together. For that very reason, they encourage abstract math thinking skills. A dime doesn't look like it's worth more than a nickel; it just is worth more than a nickel. You have to assign a value of 10 to the dime and 5 to the nickel. This is prealgebra and advanced math at its most basic; assigning values and making calculations based on those values.
A word more about the value of abstract thinking. The National Council of Teachers of Mathematics has been for some time promoting the use of hands-on math manipulatives designed to help children think about math concretely. "This five-rod is as long as five one-rods. I can see with my eyes how many one-rods it takes to make a rod of the same length as one five-rod." This is not the way math manipulatives have worked throughout history. The sheepherder who made a knot in his string for every ten sheep, or the abacus user who moved a bead to the top of his abacus to indicate "five," were using the knot or the bead to indicate abstract value. There is nothing "ten-ish" about a knot, or "five-ish" about a bead, any more than there is anything "ten-ish" about a dime or "five-ish" about a nickel. People had to think abstractly to handle the knots and beads. They couldn't just count up a number of one-rods to get the answer.
A dime does not resemble ten pennies in the least. A ten-rod resembles ten one-rods; maybe not in its color, but in having the exact same overall length and shape. Therefore, I encourage you to use rods, cubes, and even cuter manipulatives such as the Delta Fast Food math items reviewed elsewhere in this issue, to demonstrate math principles, but not to work math problems. Rather, try using coins, with all their different values. Your kids will learn the most essential math skill of all, needed in all math from algebra on up - how to solve problems where you can't simply count your way to the answer. At the moment, it will be a nickel standing for five pennies; later, it will be x standing for a number; still later, it will be x standing for an entire statement including other variables; later yet, it will be f(x) standing for a series, or a number set, or the area under a curve, and so on. All of this is really easy if you understand the concept of abstract value. But I guarantee you that a child who has always been able to stick manipulatives end-to-end or in a square to solve a problem will be totally lost when he runs into negative numbers, irrational numbers, or imaginary numbers. Don't get stuck in the concrete, when you could teach your children abstract math thinking with your pocket change.
One more point about money: even kids who struggle with numbers catch on very quickly when those numbers have two decimal places and dollar signs. I have yet to meet a kid who can't learn to shop!
Girls & Math
Research shows that American girls do noticeably worse than American boys on standardized math tests. But not homeschooled girls! Our own daughter Sarah recently scored a perfect 80 out of 80 on the math portion of the PSAT. (I admit it, that was bragging!)
The better performance of homeschooled girls probably has to do with (1) using math more in their everyday lives and (2) not being surrounded by boys who not-so-subtly prefer cute airheads to smart young misses. As long as the parents expect their daughter to do well in math, there should be nothing in the homeschool environment to hold her back.
One area that most girls do need extra help with, even at home: spatial skills. If I ask you to visualize a shape in your head, then rotate it various ways, most guys can do this with ease, but most gals can't. Two resources I have found that are a great help in improving spatial skills are:
F The Factory (Mac, Win, Apple, and DOS versions available; $89.95) and Factory Deluxe (Mac or Win CD; $89.95) software from Sunburst (1-800-321-7511). Or (for Mac only, $129.95) the Spatial Sense CD-ROM, which includes Factory, Super Factory, and Building Perspective. Check them out on www.sunburst.com.
F The most excellent D.I.M.E. Blocks ($17) and associated 3-D Build-Up books (three available for $7 each) from Timberdoodle (1-360-426-0672). This forms an entire mini-course in spatial skills, as you rotate and fit the odd-shaped blocks together. Oodles of fun, too!
Puzzles & Construction
Puzzles and construction toys are another great way to develop your spatial skills. Bill's mom was, and is, an avid puzzler, who also bought him Tinkertoys and Erector sets. Oddly enough, my parents also gave me tons of puzzles, and the very same building sets Bill grew up with.
Today, "Erector" sets are called "Meccano," and products such as Duplo and Lego bricks are mainstays of many homeschools. While Lego-like products are great for creativity, they only fit together in a few limited ways. For more advanced spatial and engineering skills, an up-to-date construction series such as Fishertechnik (available from Timberdoodle: 1-360-426-0672) or the motorized Robotix kits (available from Home Life: 1-800-346-6322) is what you need.
A Word About Words
One fact of mathematical life that nobody talks about is the nomenclature: the jargon mathematicians use. Getting a grip on the lingo as early as possible is a way for your child to "pre-digest" some of what he'll be encountering in later math courses. We were only kidding about the Baby's First Calculus course in our Homeschool Admirer parody section in this issue, because babies can't learn calculus. However, young kids can learn calculus terminology. So go ahead: "integrate" these math words into your daily life and help your children "function" better as you push them to their "limits"! (Note: the words in quotes are mathematical terms. I don't really think kids should be pushed anywhere unless they're in a baby carriage or wheelchair.)
A great book I just found that can help you with this is G is for Googol, from Tricycle Press pictured on the first page of this article ($15.95, 1-800-841-2665). This "alphabet" book is not for teaching little kiddies to read. Instead, this 57-page, oversized, fully illustrated hardcover is devoted to explaining advanced math to the young. Starting with "A is for abacus," in which we see an abacus, learn its history, and see how it works, each letter stands for one or more important topics beloved of mathematicians. I'm not talking about wimpy stuff like addition or fractions, either. Cast your ovoid oculars on this list:
Abacus, Binary, Cubit, Diamond, Equilateral, Exponent, Fibonacci, Googol, Googolplex, Hundred, "If," Jupiter, K?sberg, Light-year, M?s Strip, Nature, Obtuse, Probability, Quantity and Quality, Rhombicosidodecahedron, Symmetry, Tesselate, Unit, Venn Diagram, "When are we ever going to use this stuff, anyway?," X, Y-axis, Zillion.
Each concept is explained in easy-reading detail, with full-color drawings and diagrams. As a bonus, for each letter you'll also find a list of other math concepts starting with the letter in question. So A is for Abacus (the main entry), and also for acute, algebra, angle, art, architecture, area, asymmetry, average, and axis. No definitions are provided for the bonus list, but any parent with a smidgen of mathematical training can use this list for inspiration for further explanations and explorations.
Three last tips: (1) math puzzle books, available at bookstores and teacher's stores: (2) checkers, and (3) chess. All are great, fun ways to improve math thinking skills. Let's do it!
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